Question

from least to greatest, what are the measures of the next two angles with positive measure that are coterminal with an angle measuring 250°? and

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles can be found by adding \(360^{\circ}n\) (\(n\in\mathbb{Z}\)) to the given angle. Here, the given angle is \(250^{\circ}\) and we want positive - measure angles. For the first next positive - coterminal angle, let \(n = 1\).

$$250^{\circ}+360^{\circ}\times1$$

Step2: Calculate the first next positive - coterminal angle

$$250^{\circ}+360^{\circ}=610^{\circ}$$

Step3: Calculate the second next positive - coterminal angle

For the second next positive - coterminal angle, let \(n = 2\)

$$250^{\circ}+360^{\circ}\times2=250^{\circ}+720^{\circ}$$

$$250^{\circ}+720^{\circ}=970^{\circ}$$

Answer:

\(610\) and \(970\)